We analyze the lateral undulatory motion of a natural or artificial
snake or other slender organism that ‘‘swims’’ on land by propagating retrograde flexural waves. The governing equations for the
planar lateral undulation of a thin filament that interacts frictionally with its environment lead to an incomplete system. Closures
accounting for the forces generated by the internal muscles and
the interaction of the filament with its environment lead to a
nonlinear boundary value problem, which we solve using a combination of analytical and numerical methods. We find that the
primary determinant of the shape of the organism is its interaction
with the external environment, whereas the speed of the organism
is determined primarily by the internal muscular forces, consistent
with prior qualitative observations. Our model also allows us to
pose and solve a variety of optimization problems such as those
associated with maximum speed and mechanical efficiency, thus
defining the performance envelope of this mode of locomotion.